Application of signal detection theory to perception of differences in line length

This paper is an attempt to specify the equinormal model for application to different tasks which are currently used in psychophysics (i.e. phenomenal report, detection, and 2AFC). The same set of stimuli (pairs of horizontal colinear lines) is presented in procedures which differ by the task, the probability of the signal, and the succession of the stimuli of the set. This approach leads to the specification of the sensorial and the decisional aspects of the model.The data indicate that (1) the sensitivity index d' to differences in line length is the same function of the physical stimulus independently of paradigm, as far as the same task is concerned. However, and according to the predictions, its value becomes larger by a factor of 2 in a two alternative forced choice task; (2) d' increases with stimulus exposure time; (3) latency of responses generally decreases with increasing d', and are dissimilar for correct and incorrect responses; (4) when the temporal succession of the stimuli is random the subject's criterion, x_c, is not chosen to optimize the percentage correct, which would require a dependance of criterion upon stimulus amplitude and prior probabilities.     

study of taste perception

Taste stimulus identification was studied in order to more thoroughly examine human taste perception. Ten replicates of an array of 10 taste stimuli—NaCl, KCl, Na glutamate, quinine.HCl, citric acid, sucrose, aspartame, and NaCl-sucrose, acid-sucrose, and quinine-sucrose mixtures—were presented to normal subjects for identification from a list of corresponding stimulus names. Because perceptually similar substances are confused in identification tasks, the result was ataste confusion matrix. Consistency of identification for the 10 stimuli (T ₁₀) and for each stimulus pair (T ₂) was quantified with measures derived from information theory. Forty-two untrained subjects made an average of 57.4% correct identifications. An averageT ₁₀ of 2.25 of the maximum 3.32 bits and an averageT ₂ of 0.84 of a maximum 1.0 bit of information were transmitted. In a second experiment, 40 trained subjects per-formed better than 20 untrained subjects. The results suggested that the identification procedure may best be used to assess taste function following 1–2 training replicates. The patterns of taste confusion indicate that the 10 stimuli resemble one another to varying extents, yet each can be considered perceptually unique.     

A biased random walk model for two choice reaction times

This paper generalizes Stone's (1960, Psychometrika 25, 251–260) random walk model of two choice response times (RTs) that is based on the sequential probability ratio test (SPRT) and that predicts equal correct and incorrect RTs to the same response. The generalized version allows a bias of the type found in signal detection theory to enter directly into the accumulation process so that ambivalent evidence may be seen as slightly favoring one alternative. The resulting biased SPRT model can predict any relation between correct and incorrect mean RTs. In particular, unlike the special symmetric case of Link and Heath's (1975, Psychometrika 40, 77–105) relative judgment theory (RJT), the biased SPRT model can predict that correct mean RTs are faster for one response but slower for the other. The biased SPRT model, the classical SPRT model, and the symmetric RJT model are all fit to the data of an RT deadline experiment reported by Green and Luce (1973, Attention and performance, New York: Academic Press) and it is shown that, of the three, the biased SPRT model provides the best account. Finally, a method for incorporating the same sort of bias into RJT models is sketched out.     

Bias in self-evaluation: Signal probability effects

Two experiments examined apparent signal probability effects in simple verbal self-reports. After each trial of a delayed matching-to-sample task, young adults pressed either a “yes” or a “no” button to answer a computer-presented query about whether the most recent choice met a point contingency requiring both speed and accuracy. A successful matching-to-sample choice served as the “signal” in a signal-detection analysis of self-reports. Difficulty of matching to sample, and thus signal probability, was manipulated via the number of nonmatching sample and comparison stimuli. In Experiment 1, subjects exhibited a bias (log b) for reporting matching-to-sample success when success was frequent, and no bias or a bias for reporting failure when success was infrequent. Contingencies involving equal conditional probabilities of point consequences for “I succeeded” and “I failed” reports had no systematic effect on this pattern. Experiment 2 found signal probability effects to be evident regardless of whether referent-response difficulty was manipulated in different conditions or within sessions. These findings indicate that apparent signal probability effects in self-report bias that were observed in previous studies probably were not an artifact of contingencies intended to improve self-report accuracy or of the means of manipulating signal probability. The findings support an analogy between simple self-reports and psychophysical judgments and bolster the conclusion of Critchfield (1993) that signal probability effects can influence simple self-reports much as they do reports about external stimuli in psychophysical experiments.     

Optimal response biases and the slope of ROC curves as a function of signal intensity,signal probability,and relative payoff

Rats performed in a two-lever analogue of the yes-no psychophysical procedure. The signal consisted of of an increment in the intensity of a random noise. Correct responses were reinforced with single bursts of brain stimulation; incorrect responses produced brief periods of time-out. Receiver-operating-characteristic curves were generated at each of several signal intensities by varying either the signal probability (0.1–0.9) or the relative number of brain stimulations for correct responses (1:3–3:1). The index d’ (or d’_e) increased with the signal intensity and was independent of response bias. When the signal probability was varied, the animals optimized the number of correct trials. and hence the number of brain stimulations obtained at each level of detection. They approximated this optimum more closely as the signal intensity was reduced. When the ratio of brain stimulations was varied, the animals compromised between optimizing the number of correct trials and optimizing the number of brain stimulations obtained. The slopes of the ROC curves plotted on normal-normal coordinates frequently departed from unity, but did not change systematically with either the signal intensity or the method by which they were generated.     

The effects of age on sensory thresholds and temporal gap detection in hearing, vision, and touch

Differences in sensory function between young (n 5 42, 18—31 years old) and older (n 5 137, 60—88 years old) adults were examined for auditory, visual, and tactile measures of threshold sensitivity and temporal acuity (gap-detection threshold). For all but one of the psychophysical measures (visual gap detection), multiple measures were obtained at different stimulus frequencies for each modality and task. This resulted in a total of 14 dependent measures, each based on four to six adaptive psychophysical estimates of 75% correct performance. In addition, all participants completed the Wechsler Adult Intelligence Scale (Wechsler, 1997). Mean data confirmed previously observed differences in performance between young and older adults for 13 of the 14 dependent measures (all but visual threshold at a flicker frequency of 4 Hz). Correlational and principalcomponents factor analyses performed on the data from the 137 older adults were generally consistent with task and modality independence of the psychophysical measures.     

Decision rules and signal detectability in a reinforcement-density discrimination

Two probabilistic schedules of reinforcement, one richer in reinforcement, the other leaner, were overlapping stimuli to be discriminated in a choice situation. One of two schedules was in effect for 12 seconds. Then, during a 6-second choice period, the first left-key peck was reinforced if the richer schedule had been in effect, and the first right-key peck was reinforced if the leaner schedule had been in effect. The two schedule stimuli may be viewed as two binomial distributions of the number of reinforcement opportunities. Each schedule yielded different frequencies of 16 substimuli. Each substimulus had a particular type of outcome pattern for the 12 seconds during which a schedule was in effect, and consisted of four consecutive light-cued 3-second T-cycles, each having 0 or 1 reinforced center-key pecks. Substimuli therefore contained 0 to 4 reinforcers. On any 3-second cycle, the first center-key peck darkened that key and was reinforced with probability .75 or .25 in the richer or leaner schedules, respectively. In terms of the theory of signal detection, detectability neared the maximum possible d′ for all four pigeons. Left-key peck probability increased when number of reinforcers in a substimulus increased, when these occurred closer to choice, or when pellets were larger for correct left-key pecks than for correct right-key pecks. Averaged over different temporal patterns of reinforcement in a substimulus, substimuli with the same number of reinforcers produced choice probabilities that matched relative expected payoff rather than maximized one alternative.     

Adaptive criterion setting in perceptual decision making

Pigeons responded in a perceptual categorization task with six different stimuli (shades of gray), three of which were to be classified as "light" or "dark", respectively. Reinforcement probability for correct responses was varied from 0.2 to 0.6 across blocks of sessions and was unequal for correct light and dark responses. Introduction of a new reinforcement contingency resulted in a biphasic process of adjustment: First, choices were strongly biased towards the favored alternative, which was followed by a shift of preference back towards unbiased choice allocation. The data are well described by a signal detection model in which adjustment to a change in reinforcement contingency is modeled as the change of a criterion along a decision axis with fixed stimulus distributions. Moreover, the model shows that pigeons, after an initial overadjustment, distribute their responses almost optimally, although the overall benefit from doing so is extremely small. The strong and swift effect of minute changes in overall reinforcement probability precludes a choice strategy directly maximizing expected value, contrary to the assumption of signal detection theory. Instead, the rapid adjustments observed can be explained by a model in which reinforcement probabilities for each action, contingent on perceived stimulus intensity, determine choice allocation.     

An Evaluation of the Effects of Graphic Aids in Improving Decision Accuracy in a Continuous Treatment Design

Educators, school psychologists, and other professionals must evaluate student progress and decide to continue, modify, or terminate instructional programs to ensure student success. For this purpose, progress-monitoring data are often collected, plotted graphically, and visually analyzed. The current study evaluated the impact of three common formats for visual analysis (scatter plots, scatter plots with trend lines, and scatter plots with trend and aim lines) on the decision accuracy of 52 novice analysts. All participants viewed 18 time-series graphs that depicted student growth on a continuous metric (e.g., oral reading fluency). Participants rated each graph as depicting substantial progress, minimal progress, or no progress. The magnitude of the true slope for each graph was fixed to 3.00 (substantial progress), 0.75 (minimal progress), or 0 (no progress). Inferential analyses were used to determine the probability of a participant correctly identifying different magnitudes of trend in the presence of different visual aids (no visual aid, trend line, and trend line with aim line). The odds of correctly identifying trend were influenced by visual aid (p < .01) and trend magnitude (p < .01). The addition of a trend line resulted in a sharp increase in the probability of making a correct decision. Graphs depicting minimal progress reduced the probability of a correct decision.     

A model of three-choice discrimination learning under complete and incomplete feedback conditions

The Bower and Trabasso model of concept identification was extended to cover problems in which three stimuli were presented simultaneously and S pointed to the one he thought was correct. The E gave complete feedback by indicating the correct stimulus, or incomplete feedback by saying “correct” or “wrong.” The model accurately accounted for the significant difference in total errors between the two feedback conditions by incorporating process assumptions reflecting the logical difference in information content of the two types of feedback. Using a single set of parameter estimates, the model made satisfactory quantitative predictions of several statistics for both feedback conditions. Some deviations from the model's predictions were found in the length of terminal error runs, indicating that Ss were possibly using memory more extensively than posited by the model.     

Effects of a coactor's prediction on latencies to predict and indentify stimuli

On each of 300 trials E's confederate (C) verbalized which of two stimuli would occur; then S made a prediction. Following each presentation, S and C pulled a trigger to identify the stimulus. Two latencies were measured: the interval between C's and S's prediction (prediction time), and the interval between stimulus presentation and S's identification response (choice RT). Prediction times were significantly shorter when S's prediction agreed rather than disagreed with C's prediction, when S's preceding prediction was correct rather than incorrect, and when S was female rather than male. Choice RT was influenced by distributions of C's stimulus predictions and C's prediction outcomes in directions supporting an expectancy model.     

Component probability and component reinforcer rate as biasers of free-operant detection

Six pigeons were trained on multiple schedules whose components were concurrent variable-interval extinction and concurrent extinction variable-interval schedules. In Experiments 1a and 1b the stimuli signaling the components were two different light intensities, and in Experiments 2a and 2b they were two identical intensities. The components of the multiple schedule changed probabilistically after each reinforcer. In Experiments 1a and 2a, the probability of presenting the components was varied over five conditions and a replication. In Experiments 1b and 2b, the component probability was .5 and the component reinforcer rates were varied systematically over five conditions and a replication. The data, analyzed according to the Davison-Tustin behavioral detection model, confirmed that the discriminability of the stimuli signaling the components was high when the stimuli were different, and low when the stimuli were the same. Discriminability, measured by log d, was unaffected by component probability variation and by component reinforcer-rate variation. When discriminability was high, bias, or the response allocation between the two keys, was more strongly affected by variation of reinforcer rate within components than by variation of component probability, but the reverse was found when discriminability was low. The results suggest that free-operant detection performance is controlled by the rates of reinforcers in periods of time in which stimuli signal differential contingencies. These periods comprise the components when the component stimuli are discriminable, and comprise the total session when the components are indiscriminable. An extension of the Davison-Tustin behavioral detection model that incorporates these results is presented.     

A Signal Detection Model for Multiple-Choice Exams

A model for multiple-choice exams is developed from a signal-detection perspective. A correct alternative in a multiple-choice exam can be viewed as being a signal embedded in noise (incorrect alternatives). Examinees are assumed to have perceptions of the plausibility of each alternative, and the decision process is to choose the most plausible alternative. It is also assumed that each examinee either knows or does not know each item. These assumptions together lead to a signal detection choice model for multiple-choice exams. The model can be viewed, statistically, as a mixture extension, with random mixing, of the traditional choice model, or similarly, as a grade-of-membership extension. A version of the model with extreme value distributions is developed, in which case the model simplifies to a mixture multinomial logit model with random mixing. The approach is shown to offer measures of item discrimination and difficulty, along with information about the relative plausibility of each of the alternatives. The model, parameters, and measures derived from the parameters are compared to those obtained with several commonly used item response theory models. An application of the model to an educational data set is presented.     

Belief, knowledge, and uncertainty: A cognitive perspective on subjective probability

This paper presents a cognitive analysis of subjective probability judgments and proposes that these are assessments of belief-processing activities. The analysis is motivated by an investigation of the concepts of belief, knowledge, and uncertainty. Judgment and reasoning are differentiated, Toulmin's (1958) theory of argument being used to explicate the latter. The paper discusses a belief-processing model in which reasoning is used to translate data into conclusions, while judgmental processes qualify those conclusions with degrees of belief. The model sheds light on traditional interpretations of probability and suggests that different characteristics of belief—likelihood and support—are addressed by different representational systems. In concluding, the paper identifies new lines of research implied by its analysis.     

A comparison of signal detection theory to the objective threshold/strategic model of unconscious perception

A key problem in unconscious perception research is ruling out the possibility that weak conscious awareness of stimuli might explain the results. In the present study, signal detection theory was compared with the objective threshold/strategic model as explanations of results for detection and identification sensitivity in a commonly used unconscious perception task. In the task, 64 undergraduate participants detected and identified one of four briefly displayed, visually masked letters. Identification was significantly above baseline (i.e., proportion correct > .25) at the highest detection confidence rating. This result is most consistent with signal detection theory's continuum of sensory states and serves as a possible index of conscious perception. However, there was limited support for the other model in the form of a predicted "looker's inhibition" effect, which produced identification performance that was significantly below baseline. One additional result, an interaction between the target stimulus and type of mask, raised concerns for the generality of unconscious perception effects.     

Confidence in word detection predicts word identification: implications for an unconscious perception paradigm

The present experiments extend the scope of the independent observation model based on signal detection theory (Macmillan & Creelman, 1991) to complex (word) stimulus sets. In the first experiment, the model predicts the relationship between uncertain detection and subsequent correct identification, thereby providing an alternative interpretation to a phenomenon often described as unconscious perception. Our second experiment used an exclusion task (Jacoby, Toth, & Yonelinas, 1993), which, according to theories of unconscious perception, should show qualitative differences in performance based on stimulus detection accuracy and provide a relative measure of conscious versus unconscious influences (Merikle, Joordens, & Stoltz, 1995). Exclusion performance was also explained by the model, suggesting that undetected words did not unconsciously influence identification responses.     

Learning models for a continuum of sensory states reexamined

Dorfman and Biderman evaluated an additive-operator learning model and some special cases of this model on data from a signal-detection experiment. They found that Kac's pure error-correction model gave the poorest fit of the special models when the predictions were generated from the maximum likelihood estimates and the initial cutoffs were set at an a priori value rather than estimated. First, this paper presents tests of an asymptotic theorem by Norman, which provide strong support for Kac's model. On the final 100 trials, every subject but one gave probability matching, and the response propcrtions appropriately normed were approximately normally distributed with variance π(1 ? π). Further analyses of the Dorfman-Biderman data based upon maximum likelihood and likelihood-ratio tests suggest that Kac's model gives a relatively good, but imperfect fit to the data. Some possible explanations for the apparent contradiction between the results of these new analyses and the original findings of Dorfman and Biderman were explored. The investigations led to the proposal that there may be nonsystematic, random drifts in the decision criterion after correct responses as well as after errors. The hypothesis gives a minor modification of the conclusions from Norman's theorem for Kac's model. It gives asymptotic probability matching for every subject, but a larger asymptotic variance than π(1 ? π), which agrees with the data. The paper also presents good Monte Carlo justification for the use of maximum likelihood and likelihood-ratio tests with these additive learning models. Results from Thomas' nonparametric test of error correction are presented, which are inconclusive. Computation of Thomas' p statistic on the Monte Carlo simulations showed that it is quite variable and insensitive to small deviations from error correction.     

Human Signal-detection Performance: Effects Of Signal Presentation Probabilities And Reinforcer Distributions

University students participated in one of four standard two-choice signal-detection experiments in which signal presentation probability was varied and the reinforcement distribution was held constant and equal. In Experiments 1, 3 and 4, subjects' performance showed a systematic response bias for reporting the stimulus presented least often. Experiments 1 and 4 showed that this effect was reliable with extended training and monetary, rather than point, reinforcement. In Experiment 2, all correct responses were signaled in some way, and this produced the opposite relationship between signal presentation probability and response bias. Experiments 1 and 3 found that explicitly deducting money (intended as punishment) for equal numbers of incorrect responses on each alternative, or varying the obtained overall rate of reinforcement, produced no clear change in response bias. The bias, shown by humans, for reporting the stimulus presented least often remains a challenge for theories of stimulus detection.